A matrix formulation of the plane elastostatic inclusion problem via geometric function theory
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915536137355264 |
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| author | Cho, Daehee Choi, Doosung Lim, Mikyoung |
| author_facet | Cho, Daehee Choi, Doosung Lim, Mikyoung |
| contents | We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these methodologies to the more general case of elastic inclusions with arbitrary Lamé constants. Our approach integrates layer potential techniques, geometric function theory, and the complex-variable formulation in plane elasticity. As a main result, we derive a matrix formulation of the elastostatic inclusion problem using basis functions defined via the exterior conformal mapping of the inclusion. This leads to a series solution framework that incorporates the geometry of the inclusion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A matrix formulation of the plane elastostatic inclusion problem via geometric function theory Cho, Daehee Choi, Doosung Lim, Mikyoung Analysis of PDEs We investigate the two-dimensional elastostatic inclusion problem in an unbounded medium. Building on the recent developments for rigid inclusions \cite{Mattei:2021:EAS} and conductivity inclusions \cite{Jung:2021:SEL}, we extend these methodologies to the more general case of elastic inclusions with arbitrary Lamé constants. Our approach integrates layer potential techniques, geometric function theory, and the complex-variable formulation in plane elasticity. As a main result, we derive a matrix formulation of the elastostatic inclusion problem using basis functions defined via the exterior conformal mapping of the inclusion. This leads to a series solution framework that incorporates the geometry of the inclusion. |
| title | A matrix formulation of the plane elastostatic inclusion problem via geometric function theory |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.15713 |